It is correct that testing isn't available at the airport at midnight (it's 5am-5pm)...
I have a friend who arrived yesterday with her family and she mentioned that they had indeed to declare their information (phone, address) and that they agree that they are subject to the 14 day quarantine unless they take the test (PCR or antigen) again and have negative results. She said they didn't mention any restrictions regarding if they could just go to the lab today...
Personally I would arrange for the test to be done at the hotel, some of the labs have the service :
Synlab mentions to call to arrange
https://www.synlab.pe/panel/prueba-de-antigeno/ but this one "
Aptus"
https://teleticket.com.pe/aptus can be scheduled online I think...